Contact process with simultaneous spatial and temporal disorder

TL;DR

This paper investigates how combined spatial and temporal disorders influence the phase transition in the one-dimensional contact process, revealing stability conditions and effects on Griffiths singularities through simulations.

Contribution

It introduces a generalized Harris criterion for stability analysis and provides detailed Monte Carlo simulation results on the critical behavior under combined disorders.

Findings

Stability of directed percolation universality class under certain disorder conditions

Alteration of Griffiths singularities due to simultaneous spatial and temporal disorder

Critical behavior characterized through large-scale simulations

Abstract

We study the absorbing-state phase transition in the one-dimensional contact process under the combined influence of spatial and temporal random disorders. We focus on situations in which the spatial and temporal disorders decouple. Couched in the language of epidemic spreading, this means that some spatial regions are, at all times, more favorable than others for infections, and some time periods are more favorable than others independent of spatial location. We employ a generalized Harris criterion to discuss the stability of the directed percolation universality class against such disorder. We then perform large-scale Monte Carlo simulations to analyze the critical behavior in detail. We also discuss how the Griffiths singularities that accompany the nonequilibrium phase transition are affected by the simultaneous presence of both disorders.